cp's OEIS Frontend

A224096 Denominators of poly-Cauchy numbers c_n^(3).

%I A224096 #37 Feb 26 2023 13:20:39
%S A224096 1,8,216,576,108000,14400,14817600,16934400,571536000,127008000,
%T A224096 101428588800,18441561600,709031939616000,12120204096000,
%U A224096 6678479808000,24932991283200,229679599076928000,818822100096000
%N A224096 Denominators of poly-Cauchy numbers c_n^(3).
%C A224096 The poly-Cauchy numbers c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the first kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^m/(m+1)^k, m=0..n).
%H A224096 Vincenzo Librandi, <a href="/A224096/b224096.txt">Table of n, a(n) for n = 0..300</a>
%H A224096 Takao Komatsu, <a href="http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1806-06.pdf">Poly-Cauchy numbers</a>, RIMS Kokyuroku 1806 (2012)
%H A224096 Takao Komatsu, <a href="http://link.springer.com/article/10.1007/s11139-012-9452-0">Poly-Cauchy numbers with a q parameter</a>, Ramanujan J. 31 (2013), 353-371.
%H A224096 Takao Komatsu, <a href="http://doi.org/10.2206/kyushujm.67.143">Poly-Cauchy numbers</a>, Kyushu J. Math. 67 (2013), 143-153.
%H A224096 T. Komatsu, V. Laohakosol, K. Liptai, <a href="http://dx.doi.org/10.1155/2013/179841">A generalization of poly-Cauchy numbers and its properties</a>, Abstract and Applied Analysis, Volume 2013, Article ID 179841, 8 pages.
%H A224096 Takao Komatsu, FZ Zhao, <a href="http://arxiv.org/abs/1603.06725">The log-convexity of the poly-Cauchy numbers</a>, arXiv preprint arXiv:1603.06725, 2016
%t A224096 Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]
%o A224096 (PARI) a(n) = denominator(sum(k=0, n, stirling(n, k, 1)/(k+1)^3)); \\ _Michel Marcus_, Nov 15 2015
%Y A224096 Cf. A006233, A222636, A224094, A224097 (numerators).
%K A224096 nonn,frac
%O A224096 0,2
%A A224096 _Takao Komatsu_, Mar 31 2013